I don't know of any launch sites significantly above sea-level, the marginal performance increase wouldn't be worth the logistical nightmare. It's easier to fly up a 747 than build a launch facility on top of a mountain.
This was part of the Plot of Halo: ODST, where fragments of the space elevator collapsed onto New Mombasa.
Twice.
Because the only known material strong enough at the time was diamond, and diamond doesn’t ablate much when falling through atmosphere.
One of the early space elevator research companies specifically designed a cable that was made by stacking successive layers of material both to slowly increase carrying capacity by building the tether in iterative layers, and hoping it would ablate or at least reach a quick terminal velocity in the case of catastrophic failure.
It is undoubtedly the case that the senior staff on that project were familiar with the Mars trilogy.
The base would need to be enormous and I'm sure the power draw would be insane, but being able to break the elevator cable into smaller lines and take the weight off of any individual strand might make it a touch more plausible without currently non-existent technologies.
What’s the downrange safety cone look like for space launch sites around the world? A little S curve in your insertion orbit would certainly waste a bit of delta V. But not all orbits are equatorial anyway.